2,132 research outputs found
Spatial Coupling of a Lattice Boltzmann fluid model with a Finite Difference Navier-Stokes solver
In multiscale, multi-physics applications, there is an increasing need for
coupling numerical solvers that are each applied to a different part of the
problem. Here we consider the case of coupling a Lattice Boltzmann fluid model
and a Finite Difference Navier-Stokes solver. The coupling is implemented so
that the entire computational domain can be divided in two regions, with the FD
solver running on one of them and the LB one on the other.
We show how the various physical quantities of the two approaches should be
related to ensure a smooth transition at the interface between the regions. We
demonstrate the feasibility of the method on the Poiseuille flow, where the LB
and FD schemes are used on adjacent sub-domains.
The same idea can be also developed to couple LB models with Finite Volumes,
or Finite Elements calculations.
The motivation for developing such a type of coupling is that, depending on
the geometry of the flow, one technique can be more efficient, less memory
consuming, or physically more appropriate than the other in some regions (e.g.
near the boundaries), whereas the converse is true for other parts of the same
system. We can also imagine that a given system solved, say by FD, can be
augmented in some spatial regions with a new physical process that is better
treated by a LB model. Our approach allows us to only modify the concerned
region without altering the rest of the computation.Comment: 10 pages, 2 figure
Bridging the computational gap between mesoscopic and continuum modeling of red blood cells for fully resolved blood flow
We present a computational framework for the simulation of blood flow with
fully resolved red blood cells (RBCs) using a modular approach that consists of
a lattice Boltzmann solver for the blood plasma, a novel finite element based
solver for the deformable bodies and an immersed boundary method for the
fluid-solid interaction. For the RBCs, we propose a nodal projective FEM
(npFEM) solver which has theoretical advantages over the more commonly used
mass-spring systems (mesoscopic modeling), such as an unconditional stability,
versatile material expressivity, and one set of parameters to fully describe
the behavior of the body at any mesh resolution. At the same time, the method
is substantially faster than other FEM solvers proposed in this field, and has
an efficiency that is comparable to the one of mesoscopic models. At its core,
the solver uses specially defined potential energies, and builds upon them a
fast iterative procedure based on quasi-Newton techniques. For a known
material, our solver has only one free parameter that demands tuning, related
to the body viscoelasticity. In contrast, state-of-the-art solvers for
deformable bodies have more free parameters, and the calibration of the models
demands special assumptions regarding the mesh topology, which restrict their
generality and mesh independence. We propose as well a modification to the
potential energy proposed by Skalak et al. 1973 for the red blood cell
membrane, which enhances the strain hardening behavior at higher deformations.
Our viscoelastic model for the red blood cell, while simple enough and
applicable to any kind of solver as a post-convergence step, can capture
accurately the characteristic recovery time and tank-treading frequencies. The
framework is validated using experimental data, and it proves to be scalable
for multiple deformable bodies
Competing Species Dynamics: Qualitative Advantage versus Geography
A simple cellular automata model for a two-group war over the same territory
is presented. It is shown that a qualitative advantage is not enough for a
minority to win. A spatial organization as well a definite degree of
aggressiveness are instrumental to overcome a less fitted majority. The model
applies to a large spectrum of competing groups: smoker-non smoker war,
epidemic spreading, opinion formation, competition for industrial standards and
species evolution. In the last case, it provides a new explanation for
punctuated equilibria.Comment: 7 pages, latex, 2 figures include
Bankruptcy Law: a Mechanism of Governance for Financially Distressed Firms.
This paper explores the various governance models for financially distressed firms. We offer a new typology of major bankruptcy models and provide a connection between this bankruptcy law puzzle and the variables depicting the governance of healthy firms in order to shed light on two topics: (1) the factors that the lawyer should consider before removing its national bankruptcy law, and (2) the risks associated with each bankruptcy model according to the economic literature on bankruptcy law. Our final aim is to test whether the various bankruptcy models detailed in the paper perform in separate economic and legal environments.Bankruptcy, Governance, Law and Economics.
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